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December  2016, 21(10): 3637-3654. doi: 10.3934/dcdsb.2016114

Weak stability for integro-differential inclusions of diffusion-wave type involving infinite delays

1. 

Vietnam Education Publishing House, 81 Tran Hung Dao, Hanoi, Vietnam

2. 

Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

3. 

Department of Mathematics, Electric Power University, 235 Hoang Quoc Viet, Hanoi, Vietnam

Received  November 2015 Revised  August 2016 Published  November 2016

We deal with the Cauchy problem associated with integro-differential inclusions of diffusion-wave type involving infinite delays. Based on the behavior of resolvent operator associated with the linear part, an explicit estimate for solutions will be established. As a consequence, the weak stability of zero solution is proved in case the resolvent operator is asymptotically stable.
Citation: Thanh-Anh Nguyen, Dinh-Ke Tran, Nhu-Quan Nguyen. Weak stability for integro-differential inclusions of diffusion-wave type involving infinite delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3637-3654. doi: 10.3934/dcdsb.2016114
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show all references

References:
[1]

Nonlinear Anal., 72 (2010), 3190-3208. doi: 10.1016/j.na.2009.12.016.  Google Scholar

[2]

Math. Methods Appl. Sci., 38 (2015), 1601-1622. doi: 10.1002/mma.3172.  Google Scholar

[3]

Ph.D. Thesis, Eindhoven University of Technology, 2001. Google Scholar

[4]

Dover Publications, New York, 2006.  Google Scholar

[5]

Dyn. Syst. Appl., 10 (2001), 89-116.  Google Scholar

[6]

Appl. Math. Lett., 23 (2010), 960-965. doi: 10.1016/j.aml.2010.04.016.  Google Scholar

[7]

J. Integral Equations Appl., 26 (2014), 145-170. doi: 10.1216/JIE-2014-26-2-145.  Google Scholar

[8]

Nonlinear Anal., 72 (2010), 1683-1689. doi: 10.1016/j.na.2009.09.007.  Google Scholar

[9]

Appl. Math. Lett., 22 (2009), 865-870. doi: 10.1016/j.aml.2008.07.013.  Google Scholar

[10]

Discrete Contin. Dyn. Syst., (Supplement) (2007), 277-285.  Google Scholar

[11]

Proc. Amer. Math. Soc., 118 (1993), 447-453. doi: 10.2307/2160321.  Google Scholar

[12]

Springer-Verlag, New York Inc., 1977.  Google Scholar

[13]

Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999. doi: 10.1137/1.9781611971088.  Google Scholar

[14]

Translated from the Russian. Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1988. doi: 10.1007/978-94-015-7793-9.  Google Scholar

[15]

Osaka J. Math., 27 (1990), 309-321.  Google Scholar

[16]

Osaka J. Math., 27 (1990), 797-804.  Google Scholar

[17]

Nonlinear Anal., 51 (2002), 765-782. doi: 10.1016/S0362-546X(01)00861-6.  Google Scholar

[18]

Funkcial. Ekvac., 21 (1978), 11-41.  Google Scholar

[19]

Springer-Verlag, New York, 1993. doi: 10.1007/978-1-4612-4342-7.  Google Scholar

[20]

Lecture Notes in Mathematics, vol. 1473, Springer-Verlag, Berlin, 1991. doi: 10.1007/BFb0084432.  Google Scholar

[21]

in: de Gruyter Series in Nonlinear Analysis and Applications, vol. 7, Walter de Gruyter, Berlin, New York, 2001. doi: 10.1515/9783110870893.  Google Scholar

[22]

J. Comput. Acoustics, 9 (2001), 1417-1436. doi: 10.1142/S0218396X01000826.  Google Scholar

[23]

Phys. Rep., 339 (2000), 1-77. doi: 10.1016/S0370-1573(00)00070-3.  Google Scholar

[24]

Europhys. Lett., 51 (2000), 492-498. doi: 10.1209/epl/i2000-00364-5.  Google Scholar

[25]

Math. Program. Ser. A, 113 (2008), 345-424. doi: 10.1007/s10107-006-0052-x.  Google Scholar

[26]

Springer-Verlag, New York, 1983. doi: 10.1007/978-1-4612-5561-1.  Google Scholar

[27]

J. Math. Anal. Appl., 382 (2011), 426-447. doi: 10.1016/j.jmaa.2011.04.058.  Google Scholar

[28]

SIAM J. Control Optim., 25 (1987), 1173-1191. doi: 10.1137/0325064.  Google Scholar

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